Overcoming the challenge of scalability has received much attention [1]}, [2]}. One class of approaches is to develop efficient algorithms based on first-order methods. For instance, a general conic solver based on alternating direction method of multipliers (ADMM) was developed in [3]}, and a sparse conic solver based on ADMM for SDPs with chordal sparsity was developed in [4]}, [5]}; see [1]} for a recent overview. While first-order methods considerably speed up the computational time at each iteration, achieving solutions of high accuracy remains a central challenge and may require unacceptable many iterations. Therefore, first-order methods are mainly suitable for applications that only require solutions of moderate accuracy.
